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• # Artykuł - szczegóły

## Studia Mathematica

2009 | 191 | 3 | 237-246

## Sublinear eigenvalue problems on compact Riemannian manifolds with applications in Emden-Fowler equations

EN

### Abstrakty

EN
Let (M,g) be a compact Riemannian manifold without boundary, with dim M ≥ 3, and f: ℝ → ℝ a continuous function which is sublinear at infinity. By various variational approaches, existence of multiple solutions of the eigenvalue problem
$-Δ_{g}ω + α(σ)ω = K̃(λ,σ)f(ω)$, σ ∈ M, ω ∈ H₁²(M),
is established for certain eigenvalues λ > 0, depending on further properties of f and on explicit forms of the function K̃. Here, $Δ_{g}$ stands for the Laplace-Beltrami operator on (M,g), and α, K̃ are smooth positive functions. These multiplicity results are then applied to solve Emden-Fowler equations which involve sublinear terms at infinity.

237-246

wydano
2009

### Twórcy

autor
• Department of Economics, University of Babeş-Bolyai, 400591 Cluj-Napoca, Romania
autor
• Institute of Mathematics "Simion Stoilow", of the Romanian Academy, 014700 Bucureşti, Romania
• Department of Mathematics, University of Craiova, 200585 Craiova, Romania